Related papers: On the existence and construction of Dulac functio…
In this paper we discuss the existence of solutions to vectorial differential inclusions. We investigate sufficient conditions for existence, more flexible than those available in the literature, so that important applications can be fitted…
This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.
We illustrate with several new applications the power and elegance of the Bendixson Dulac theorem to obtain upper bounds of the number of limit cycles for several families of planar vector fields. In some cases we propose to use a function…
We give a simple proof of a crucial lemma that is established in [1, Lemma 2.1] by induction, and plays important roles in that paper and [2].
A Lagrangian theory giving rise to a version of the Dirac-Kahler equations on curved backgrounds is considered. The principal pieces are the general fields which have values in the algebra of the Dirac matrices and satisfy a Dirac-type…
Necessary and sufficient conditions for the interlacing of the zeros of cylinder functions and their derivatives of different orders are given.
The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.
We provide necessary and sufficient conditions for operator-valued functions on arbitrary sets associated with a collection of test functions to have factorizations in several situations.
The paper is concerned with the completeness property of root functions of the Dirac operator with summable complexvalued potential and non-regular boundary conditions. We also obtain explicit form for the fundamental solution system of the…
Sufficient conditions for linear electrodynamics with real Dirac field are derived.
The paper is concerned with the basis properties of root function systems of the Dirac operator with a complex-valued summable potential. We establish a necessary condition of convergence of corresponding spectral expansions.
We give a sufficient condition for the existence of a quadratic exponential vector with test function in L2(Rd) ? L?(Rd). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique…
We demonstrate existence and uniqueness of Picard--Vessiot extensions satisfying prescribed properties, for systems of linear differential equations over a field satisfying the same properties, under some closure assumptions on the field of…
During the last years the authors have studied the number of limit cycles of several families of planar vector fields. The common tool has been the use of an extended version of the celebrated Bendixson-Dulac Theorem. The aim of this work…
The article provides proofs for the regularity of Dirac eigenfunctions, subject to MIT boundary conditions employed on various types of open sets ranging from smooth ones to convex polygons in two dimensions, as well as on half-space and…
The electric or magnetic field of an ideal dipole is known to have a Dirac delta function at the origin. The usual textbook derivation of this delta function is rather ad hoc and cannot be used to calculate the delta-function structure for…
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential…
The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions…
Dirac delta function of matrix argument is employed frequently in the development of diverse fields such as Random Matrix Theory, Quantum Information Theory, etc. The purpose of the article is pedagogical, it begins by recalling detailed…
We introduce several sufficient conditions to guarantee the existence of the Milnor vector field for new classes of singularities of map germs. This special vector field is related with the equivalence problem of the Milnor fibrations for…